Ajima-Malfatti Points


The lines connecting the vertices and corresponding circle-circle intersections in Malfatti's problem coincide in a point X_(179) called the first Ajima-Malfatti point (Kimberling and MacDonald 1990, Kimberling 1994). This point has triangle center function


Similarly, letting A^(''), B^(''), and C^('') be the excenters of DeltaABC, then the lines A^'A^(''), B^'B^(''), and C^'C^('') are coincident in another point called the second Ajima-Malfatti point, which is Kimberling center X_(180) (but is at present given erroneously in Kimberling's tabulation).

These points are sometimes simply called the Malfatti points (Kimberling 1994).

See also

Malfatti Circles, Malfatti's Problem, Sangaku Problem, Tangent Circles

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Fukagawa, H. and Pedoe, D. Japanese Temple Geometry Problems. Winnipeg, Manitoba, Canada: Charles Babbage Research Foundation, 1989.Goldberg, M. "On the Original Malfatti Problem." Math. Mag. 40, 241-247, 1967.Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Kimberling, C. "1st and 2nd Ajima-Malfatti Points.", C. "Encyclopedia of Triangle Centers: X(179)=1st Ajima-Malfatti Point.", C. "Encyclopedia of Triangle Centers: X(180)=2nd Ajima-Malfatti Point.", C. and MacDonald, I. G. "Problem E 3251 and Solution." Amer. Math. Monthly 97, 612-613, 1990.

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Ajima-Malfatti Points

Cite this as:

Weisstein, Eric W. "Ajima-Malfatti Points." From MathWorld--A Wolfram Web Resource.

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